If A is an angle in the first quadrant and arc sin(x) = A, find arc cos(x).

Answer 1

sinA = x

cos(90-A) = sinA = x

arccosx = 90-A

for example

let A = 30 degrees, x = 1/2

sin30 = 1/2

arcsin(1/2) = 30

cos(90-30) = cos60 = 1/2

arccos(1/2) = 60 = 90-30 = 90-A

arccosx= 90-A

graphically shift the cosine curve to the right 90 degrees and you have the sine curve

cos(90-A) = sinA

cos(90-90) = cos0 = 1 = sin90 = 1